The proposed coarse-to-fine method was evaluated with many stereo pairs obtained from public data sets in the internet. Several output disparity maps computed by the proposed method are shown in FIGURE6.1 and 6.2. The first row in FIG- URE6.1 is the left and the right image of an example stereo pair, this stereo pairs and the pair that was used to produce the map in FIGURE6.2(h) were acquired from the authors of [124]. The left and the right image in the second row in FIG- URE6.1 are the disparity map of Layer 1 and Layer 0 respectively. Each row in FIGURE6.2 shows only the left image of stereo pairs and its corresponding dis- parity image on the left and the right column respectively. In FIGURE6.2, Image (a) and (c) were downloaded from the web-site mentioned in [89], and Image (e) is a frame in the artificial image sequence mentioned in Section 6.1. Because the disparity maps in FIGURE6.1and 6.2were obtained by using Dynamic Program- ming in only the horizontal direction, strikeout lines still appear in the disparity maps.
The parameters that were used to compute the disparity maps in FIGURE6.1and 6.2 are shown in Table6.1. Where, the relationship between aggregation window sizes (Wu, Wv) and sampling steps (Δu, Δv, Δd) should satisfy the condition explained in Section3.2. For example, the sampling step of the last layer (Layer 0 in this experiment) has to be 1 in order to obtain the finest disparity map, and sampling steps of the previous layers (Layer 1 in this experiment) have to be less than or equal to the size of the corresponding aggregation windows which is selected based on empirical manner (15 pixels in this experiment).
Table 6.1: Parameters used to compute disparity maps
Disparity range: [0 , 60]
Number of layers: 2
Disparity selection method: DP
Smooth factor used in DP 50
Layer Wu Wv Δu Δv Δd
1 15 15 15 15 15
0 7 7 1 1 1
Chapter 6. Experimental Results and Discussions 107
(a) (b)
(c) (d)
Figure 6.1: Qualitative illustration of the proposed coarse-to-fine method.
First row: the left and the right image. Second row: the disparity images of the two layers.
In order to compare the computation time, a well-known test-bed for the stereo matching algorithms in [89] was used as the reference. The test-bed was also implemented by C++ as the proposed method, but it ran directly on Windows instead of MATLAB as the proposed method did. Both of the test-bed and the proposed method ran on the same computer system as mentioned in Section 6.1.
The computation time of the proposed method and the referred test-bed’s method are sketched in FIGURE6.3. The data shown in FIGURE6.3 was obtained by matching image in FIGURE6.2(e) and its right image, which have a resolution of 512×512 pixels and 1 color channel. FIGURE6.3indicates that the computation time of the proposed method change slowly when the total number of possible disparities increases; this result can be explained by the fact that the search for disparity layers is performed only in limited regions of the whole disparity space.
Otherwise, the computation time of exhaustive computation methods like the referred test-bed’s method will increase proportionally to the width of disparity search ranges. This can be explained by the fact that, in theory, the computational complexity of exhaustive computation methods is O(U∗V ∗D) for WTA and DP,
Chapter 6. Experimental Results and Discussions 108
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure 6.2: Qualitative illustration of the proposed coarse-to-fine method.
Left column: the left images of the pairs. Right column: the final disparity images.
Chapter 6. Experimental Results and Discussions 109 and O(U ∗V ∗D2) for SO. The experiment as exemplified in FIGURE6.3 well demonstrates that the proposed method is very efficient in computing disparity maps for high resolution stereo images, which have wide disparity search ranges.
Figure 6.3: Quantitative comparison for the computation time.
The artificial sequence was used to evaluate the quality of output disparity maps because ground-truth images are available for quantitative comparison. Disparity maps for the artificial sequence were computed by the proposed method as well as by the referred test-bed’s. The proposed method is computed using the parameters in Table6.1. The averaged absolute mean error was used for the comparison. The errors for 300 pairs of stereo images in the artificial sequence are illustrated in FIGURE6.4. That figure shows that the errors of the proposed method are smaller than the corresponding errors of the referred test-bed’s method. This result can be explained by the effect of using multiple aggregation windows with different sizes (15×15 and 7×7 in this experiment). That effect was also explained in [125].
For instance, layer 1 works as a refinement step for layer 0 in this experiment, so the proposed method can produce a better accuracy. In FIGURE6.4, the errors for frames from 50 to 90 are larger then the errors for the other frames because in those frames the crossing vehicle leaves the cameras field of view, this phenomenon conforms to the conclusion in [127].
Although recent research works can perform the disparity computation efficiently by utilizing the powerful computation capacity of special hardwares such as FPGA, DSP, and SSE [89,118,124], those methods need to access to so many unnecessary locations in disparity spaces. The proposed method in this paper has demonstrated that the quality of output disparity maps is still ensured when the computation is
Chapter 6. Experimental Results and Discussions 110
Figure 6.4: Quantitative comparison for the accuracy of disparity images.
done at only sampled locations of disparity spaces. As indicated in FIGURE6.3, the proposed method has not used special hardwares, but it can perform the disparity computation very efficiently for a wide disparity range of 301 pixels.